document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115561>Question 115561</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780132321020/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Automotive trades:<BR>\n" );
document.write( "Total piston displacement is given by the following formula:\r<BR>\n" );
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document.write( "P.D. = piD^2LN  (pi is over 4)\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "P.D. = piston displacement in cubic in.<BR>\n" );
document.write( "D = diameter of bore of cylinder<BR>\n" );
document.write( "L= length of stroke, in inches<BR>\n" );
document.write( "N = Number of cylinders\r<BR>\n" );
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document.write( "A. P.D. = 400 cu in. L = 4.5 in. N = 8\r<BR>\n" );
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document.write( "B. P.D. = 392.7 cu. in. L = 4 in. N = 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84116 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the formula for total piston displacement as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PD+=+%28%28pi%2AD%5E2%29%2F4%29%2AL%2AN ALIGN=MIDDLE  ALT=\"PD+=+%28%28pi%2AD%5E2%29%2F4%29%2AL%2AN\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's analyze this formula just a little to see what it is telling us. <BR>\n" );
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document.write( "The part of the formula that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2AD%5E2%2F4 ALIGN=MIDDLE  ALT=\"pi%2AD%5E2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is just the old geometry formula for finding <BR>\n" );
document.write( "the area of a circle when you are given the diameter of the circle. In this case you are given<BR>\n" );
document.write( "the diameter of the bore, and you are calculating the cross-sectional area of the cylinder.<BR>\n" );
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document.write( "Next you multiply that area by the length of the stroke. What you are finding by doing this<BR>\n" );
document.write( "is the volume displacement for a single cylinder. What you have done this far is just the<BR>\n" );
document.write( "same as the old geometry problem of finding the volume of right cylinder by multiplying<BR>\n" );
document.write( "the area of its circular base times the height of the cylinder.<BR>\n" );
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document.write( "Finally you multiply this by volume for a single cylinder in the car by the number of cylinders<BR>\n" );
document.write( "in the engine to find the total volume displacement or Piston Displacement.<BR>\n" );
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document.write( "You give two problems in which you specify the total Piston Displacement, the length of the stroke,<BR>\n" );
document.write( "and the number of cylinders. I guess that you want to find the diameter of the cylinder bore.<BR>\n" );
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document.write( "For the first problem the total PD is 400 cubic inches ...(about 6.6 liter - a gas guzzler).<BR>\n" );
document.write( "The length of the stroke is 4.5 inches, and there are 8 cylinders. Substituting all these <BR>\n" );
document.write( "values into the equation you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+%28%28pi%2AD%5E2%29%2F4%29%2A4.5%2A8 ALIGN=MIDDLE  ALT=\"400+=+%28%28pi%2AD%5E2%29%2F4%29%2A4.5%2A8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The L and the N multiply out to give 4.5 * 8 = 36. Substitute this into the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+%28%28pi%2AD%5E2%29%2F4%29%2A36 ALIGN=MIDDLE  ALT=\"400+=+%28%28pi%2AD%5E2%29%2F4%29%2A36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of this equation by 36 to get rid of the factor 36 on the right side.<BR>\n" );
document.write( "On the left side 400 divided by 36 becomes 11.11111111. And on the right side the 36 is<BR>\n" );
document.write( "divided by 36 which equals 1. So the reduced equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.11111111+=+%28pi%2AD%5E2%29%2F4 ALIGN=MIDDLE  ALT=\"11.11111111+=+%28pi%2AD%5E2%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the denominator of 4 on the right side by multiplying both sides of the equation<BR>\n" );
document.write( "by 4 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44.44444444+=+pi%2AD%5E2 ALIGN=MIDDLE  ALT=\"44.44444444+=+pi%2AD%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of the equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > which approximately equals 3.141592654. <BR>\n" );
document.write( "The left side of the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44.44444444%2F3.141592654 ALIGN=MIDDLE  ALT=\"44.44444444%2F3.141592654\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this divides out to give <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.14710605 ALIGN=MIDDLE  ALT=\"14.14710605\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the right side the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Fpi ALIGN=MIDDLE  ALT=\"pi%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes just a factor of 1. So the equation you are left <BR>\n" );
document.write( "with is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.14710605+=+D%5E2 ALIGN=MIDDLE  ALT=\"14.14710605+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for D by taking the square root of both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%2814.14710605%29+=+3.76126389 ALIGN=MIDDLE  ALT=\"D+=+sqrt%2814.14710605%29+=+3.76126389\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer to this problem is that the bore has a diameter of 3.76126389 inches. You<BR>\n" );
document.write( "can round off this answer to the accuracy you need.<BR>\n" );
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document.write( "The second problem is the same ... only the numbers have changed ... This time the equation with<BR>\n" );
document.write( "the appropriate numbers inserted is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=392.7+=+%28%28pi%2AD%5E2%29%2F4%29%2A4%2A6 ALIGN=MIDDLE  ALT=\"392.7+=+%28%28pi%2AD%5E2%29%2F4%29%2A4%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And the stroke times the number of cylinders is 24 ... making the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=392.7+=+%28%28pi%2AD%5E2%29%2F4%29%2A24 ALIGN=MIDDLE  ALT=\"392.7+=+%28%28pi%2AD%5E2%29%2F4%29%2A24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 24:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16.3265+=+%28pi%2AD%5E2%29%2F4 ALIGN=MIDDLE  ALT=\"16.3265+=+%28pi%2AD%5E2%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply both sides by 4:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65.45+=+%28pi%2AD%5E2%29 ALIGN=MIDDLE  ALT=\"65.45+=+%28pi%2AD%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20.83338205+=+D%5E2 ALIGN=MIDDLE  ALT=\"20.83338205+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for D by taking the square root of both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+sqrt%2820.83338205%29+=+4.564359983 ALIGN=MIDDLE  ALT=\"D+=+sqrt%2820.83338205%29+=+4.564359983\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So this time the diameter of the cylinder bore is 4.564359983 inches ... (probably not<BR>\n" );
document.write( "a very economical 6 cylinder engine).<BR>\n" );
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document.write( "Hope this is what you were looking for and it helps you to understand the problem. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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